36.3.12 problem 13

Internal problem ID [6333]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.4, Exact equations. Exercises. page 64
Problem number : 13
Date solved : Monday, January 27, 2025 at 01:56:51 PM
CAS classification : [_linear]

\begin{align*} {\mathrm e}^{t} \left (y-t \right )+\left (1+{\mathrm e}^{t}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 19

dsolve(exp(t)*(y(t)-t)+(1+exp(t))*diff(y(t),t)=0,y(t), singsol=all)
 

\[ y = \frac {\left (t -1\right ) {\mathrm e}^{t}+c_1}{1+{\mathrm e}^{t}} \]

✓ Solution by Mathematica

Time used: 0.081 (sec). Leaf size: 23

DSolve[Exp[t]*(y[t]-t)+(1+Exp[t])*D[y[t],t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {e^t (t-1)+c_1}{e^t+1} \]